The scaling in the previous equation is clearly unfavorable compared even with the trapezoidal rule. We saw that the trapezoidal rule carries a truncation error $$ \mathrm{error}\sim O(h^2), $$ with \( h \) the step length. In general, methods based on a Taylor expansion such as the trapezoidal rule or Simpson's rule have a truncation error which goes like \( \sim O(h^k) \), with \( k \ge 1 \). Recalling that the step size is defined as \( h=(b-a)/N \), we have an error which goes like $$ \mathrm{error}\sim N^{-k}. $$